An iterative thresholding algorithm for linear inverse problems with mixed multi-constraints and its applications

TL;DR

This paper introduces an iterative thresholding algorithm designed for linear inverse problems involving multiple constraints, extending previous minimization frameworks to better handle complex practical applications such as image processing.

Contribution

It generalizes existing minimization methods to accommodate multiple constraints, providing a new approach applicable to various inverse problems with multi-frames, multi-wavelets, or multi-constraints.

Findings

Applicable to image processing problems with multiple constraints

Provides a unified framework for multi-constraint inverse problems

Enhances solution accuracy in practical applications

Abstract

In this paper, we will present a generalization for a minimization problem from I. Daubechies, M. Defrise, and C. Demol [3]. This generalization is useful for solving many practical problems in which more than one constraint are involved. In this regard, we will conclude the findings of many papers (most of which are on image processing) from this generalization. It is hoped that the approach proposed in this paper will be a suitable reference for some applied works where multi-frames, multi-wavelets, or multi-constraints are present in linear inverse problems.